Robust and cost-effective distribution is critical to any home delivery network growing company, both to meet demand under normal conditions and to adapt to temporary disruptions. Home healthcare is anticipated to be a rapidly growing modality of healthcare, itself the largest industry in the US and rife with optimization needs in areas such as logistics, scheduling, and supply chains. We develop two mixed integer programming models to optimize forward storage locations in the supply chain of a national consumable medical supplies company with consistent monthly repeating demand, temporary disruption of facility operations, and remote international manufacturers. Modified p-median single and multi-echelon models are used to determine optimal locations of warehouses and distribution facilities that minimize total transportation cost, with 13% savings in one application (approximately $1.4 million annually). Sensitivity analyses to a range of scenarios suggest that the optimal solution is robust across a number of potential scenarios.
References
[1]
Gutiérrez, E.V., Gutiérrez, V. and Vidal, C.J. (2013) Home Health Care Logistics Management: Framework and Research Perspectives. International Journal of Industrial Engineering and Management, 4, 173-182.
[2]
Liu, R., Xie, X. and Garaix, T. (2013) Weekly Home Health Care Logistics. 2013 10th IEEE International Conference on Networking, Sensing and Control, Evry, 10-12 April 2013, 282-287.
[3]
Cryer, L., Shannon, S.B., Van Amsterdam, M. and Leff, B. (2012) Costs for “Hospital at Home” Patients Were 19 Percent Lower, with Equal or Better Outcomes Compared to Similar Inpatients. Health Affairs, 31, 1237-1243.
https://doi.org/10.1377/hlthaff.2011.1132
[4]
Baumol, W. and Wolfe, P. (1958) A Warehouse-Location Problem. Operations Research, 6, 252-263. https://doi.org/10.1287/opre.6.2.252
[5]
Melkote, S. and Daskin, M.S. (2001) An Integrated Model of Facility Location and Transportation Network Design. Transportation Research Part A: Policy and Practice, 35, 515-538. https://doi.org/10.1016/S0965-8564(00)00005-7
[6]
Nagurney, A. (2010) Optimal Supply Chain Network Design and Redesign at Minimal Total Cost and with Demand Satisfaction. International Journal of Production Economics, 128, 200-208. https://doi.org/10.1016/j.ijpe.2010.07.020
[7]
SteadieSeifi, M., Dellaert, N.P., Nuijten, W., Van Woensel, T. and Raoufi, R. (2014) Multimodal Freight Transportation Planning: A Literature Review. European Journal of Operational Research, 233, 1-15. https://doi.org/10.1016/j.ejor.2013.06.055
[8]
Campbell, J.F. (1994) Integer Programming Formulations of Discrete Hub Location Problems. European Journal of Operational Research, 72, 387-405.
https://doi.org/10.1016/0377-2217(94)90318-2
[9]
Marianov, V., Serra, D. and ReVelle, C. (1999) Location of Hubs in a Competitive Environment. European Journal of Operational Research, 114, 363-371.
https://doi.org/10.1016/S0377-2217(98)00195-7
[10]
O’Kelly, M.E. (1987) A Quadratic Integer Program for the Location of Interacting Hub Facilities. European Journal of Operational Research, 32, 393-404.
https://doi.org/10.1016/S0377-2217(87)80007-3
[11]
Weber, A. and Friedrich, C.J. (1929) Alfred Weber’s Theory of Location of Industries. The University of Chicago Press, Chicago.
[12]
Dearing, P.M. and Francis, R.L. (1974) A Minimax Location Problem on a Network. Transportation Science, 8, 333-343. https://doi.org/10.1287/trsc.8.4.333
[13]
ReVelle, C.S. and Eiselt, H.A. (2005) Location Analysis: A Synthesis and Survey. European Journal of Operational Research, 165, 1-19.
https://doi.org/10.1016/j.ejor.2003.11.032
[14]
Beamon, B.M. (1998) Supply Chain Design and Analysis: Models and Methods. International Journal of Production Economics, 55, 281-294.
https://doi.org/10.1016/S0925-5273(98)00079-6
[15]
Bozkaya, B., Zhang, J. and Erkut, E. (2002) An Efficient Genetic Algorithm for the p-Median Problem. Springer-Verlag, Berlin, 179-205.
https://doi.org/10.1007/978-3-642-56082-8_6
[16]
Hakimi, S.L. (1964) Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph. Operations Research, 12, 450-459.
https://doi.org/10.1287/opre.12.3.450
[17]
Hansen, P. and Mladenovic, N. (1997) Variable Neighborhood Search for the p-Median. Location Science, 5, 207-226.
https://doi.org/10.1016/S0966-8349(98)00030-8
[18]
Cheong, M.L.F., Bhatnagar, R. and Graves, S.C. (2007) Logistics Network Design with Supplier Consolidation Hubs and Multiple Shipment Options. Journal of Industrial and Management Optimization, 3, 51-69.
https://doi.org/10.3934/jimo.2007.3.51
[19]
Goldman, A.J. (1969) Optimal Locations for Centers in a Network. Transportation Science, 3, 352-360.
[20]
Skorin-Kapov, D., Skorin-Kapov, J. and O’Kelly, M. (1996) Tight Linear Programming Relaxations of Uncapacitated p-Hub Median Problems. European Journal of Operational Research, 94, 582-593. https://doi.org/10.1016/0377-2217(95)00100-X
[21]
Fotheringham, A. and O’Kelly, M.E. (1989) Spatial Interaction Models: Formulations and Applications. Kluwer Academic Publishers, Dordrechit.
[22]
Goldman, A.J. (1971) Optimal Center Location in Simple Networks. Transportation Science, 5, 212-221. https://doi.org/10.1287/trsc.5.2.212
[23]
O’Kelly, M.E., Bryan, D., Skorin-Kapov, D. and Skorin-Kapov, J. (1996) Hub Network Design with Single and Multiple Allocation: A Computational Study. Location Science, 4, 125-138. https://doi.org/10.1016/S0966-8349(96)00015-0
[24]
Kariv, O. and Hakimi, S. (1979) An Algorithmic Approach to Network Location Problems. II: The p-Medians. SIAM Journal on Applied Mathematics, 37, 539-560.
https://doi.org/10.1137/0137041
[25]
Hansen, P., Peeters, D. and Thisse, J.F. (1983) Public Facility Location Models: A Selective Survey. Locational Analysis of Public Facilities, Amsterdam, 223-262.
